Against a cultural background of morbid touchiness about references to gender, race, etc., the word bitch is a lens into what’s going on beneath the fig leaf of political correctness.
Calling a particular person a bitch in private is bad manners but if you disregard all the ostentatious political posturing, the visceral reaction most people have to bitch used in that way isn’t much different from their reaction to gender-neutral epithets such asshole, or to male-specific insults such as prick, or dick. Bitch, used in this way, is an insult to a particular person, and after all, offending is the goal. Bitch is not nearly as shocking to the ears as the c-word-that-dare-not-be-spoken (here in the US, anyway—in the UK cunt is practically a term of endearment when applied to a man.)
Gender-specific insults are tricky but you have to be willfully obtuse to deny that much obnoxious behavior has gender. I’m not talking about the gender of the obnoxious person, but the behavior itself. Being a prick is definitely a yang personality trait and being a bitch is yin, regardless of the sex of the insulted or insulting party. Asshole, on the other hand, is neuter, despite the fact that many more men than women are assholes. Assholes are like happy families but the epithet pig can connote at least three distinct kinds of obnoxiousness, one specific to each gender plus one neuter. I like the gender-specificity of all of these words and usages and doubly applaud their use when the target is not gender-consistent with the epithet. The comprehensibility of cross-gender insults is a sign of progress in the relationship of the sexes.